Question

How do you express `2x+y=8` in the form `y=mx+b`, what is the slope and y intercept?

Answer 1

See full explanation below.

Explanation:

To express this equation in the form of `y = color(red)(m)x + color(blue)(b)` you need to subtract #color(green)(2x) from each side of the equation:

`2x - color(green)(2x) + y = color(green)(2x) + 8`

`0 + y = -2x + 8`

`y = -2x + 8`

This equation is now in the slope intercept form.

The slope-intercept form of a linear equation is:

`y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b` is the y-intercept value.

Looking at our equation:

`y = color(red)(-2)x + color(blue)(8)`

Therefore:

`color(red)(m = -2)` so the slope is `color(red)(-2)`

`color(blue)(b = 8)` so the y-intercept is `color(blue)(8)` or (`color(blue)(0)`,`color(blue)( 8)`)